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A new way of constructing N-way arbiters is proposed. The main idea is to perform arbitrations between all pairs of requests, and then make decision on what grant to issue based on their outcomes. Crucially, all the mutual exclusion elements in such an arbiter work in parallel. This `flat' arbitration is prone to new threats such as formation of cycles (leading to deadlocks), but at the same time opens up new opportunities for designing arbitration structures with different decision policies due to the availability of the global order relation between requests. To facilitate resolution of such cycles and further developments in the context of flat arbitration, the paper presents new theoretical results, including a proof of correctness of a generic structure for the N-way arbiter decision logic. In particular, in some situations a request that lost some pairwise arbitrations has to be granted to avoid a deadlock.